The Hilbert transform: Applications to atomic spectra

TL;DR

This paper demonstrates how the Hilbert transform can be used as an alternative to Kramers-Kronig relations for extracting optical properties like refractive index and group delay from transmission spectra, simplifying experimental procedures.

Contribution

It introduces the application of the Hilbert transform to atomic spectra for indirect measurement of optical properties, offering a mathematically equivalent but potentially simpler method.

Findings

Hilbert transform effectively retrieves refractive index from spectra.

The method avoids complex experimental setups.

Application to Cs vapor spectra confirms practical utility.

Abstract

In many areas of physics, the Kramers-Kronig (KK) relations are used to extract information about the real part of the optical response of a medium from its imaginary counterpart. In this paper we discuss an alternative but mathematically equivalent approach based on the Hilbert transform. We apply the Hilbert transform to transmission spectra to find the group and refractive indices of a Cs vapor, and thereby demonstrate how the Hilbert transform allows indirect measurement of the refractive index, group index and group delay whilst avoiding the use of complicated experimental set ups.